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A nice touch

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Sean McAfee
October 30, 2021 19:38
A nice touch
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Recently I was golfing the "hyperfactorial," defined for a number 𝑛 as
𝑛**𝑛 × (𝑛-1)**(𝑛-1) × (𝑛-2)**(𝑛-2) × ... × 1.  I created a quite
concise Raku function:

    { [*] [\*] $_...1 }

The only problem was that this function returns zero for a zero input,
whereas the hyperfactorial of 0 is supposed to be 1.  Of course I could
have just handled zero as a special case, but I hoped to find something
comparably short.  After a bit of thought I tried reversing both the range
and the operator:

    { [*] [\R*] 1..$_ }

It worked!  But I couldn't quite see how.  * is commutative, so isn't it
exactly the same as R*?

It turns out, in Raku it isn't quite the same.  On the operators page, I
found that the R metaoperator produces an operator that reverses the order
of the arguments, but *also* has the opposite associativity.  So, for
example, [\R*] 1..4 reduces from the right, producing the list (4, 12, 24,
24).  Somehow I had formed the idea that Raku operators are left-, right-,
or list-associative, but I was wrong.

Anyway, pretty cool!

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